Transportation or CT Scanners: A Theory and Method of Health Resources Allocation Howard P. Greenwald, John M. Woodward and David H. Berg Cost containment and access to appropriate care are the two most frequently discussed issues in contemporary health policy. Conceiving of the health services available in specific regions as "packages" of diverse items, the authors of this article consider the economic trade-offs among the various resources needed for appropriate care. In the discussion that follows, we examine the trade-offs between two divergent offerings of the health care system: high technology medicine and support services. Specifically, we examine several strategies designed to achieve an optimal mix of investments in CT scanners and transportation resources in the South Chicago region. Using linear programming as a method for examining th-ese options, the authors found that 1) the proper location of CT scanners is as important for cost containment as optimal number, and 2) excess capacity in the utilization of a single resource-CT scanners-need not imply inefficiency in the overall delivery of the service. These findings help demonstrate the importance of viewing health care as a package of interrelated services, both for achieving cost containment and for providing access to appropriate care.
Two central issues have emerged from the furor over health policy: cost containment and access to quality care. Commentaries on the "health crisis" almost invariably commence with a discussion of costs. They cite figures to illustrate the seemingly malignant domination by health services of ever greater portions of the gross national product [1] and decry the breakdown of the market's capacity to serve as an effective immunological mechanism against this process [2-41. Those concerned with access-access not merely to health professionals and facilities, but to the most appropriate forms of care-report inadequate numbers of physicians in needed specialties [5], unreasonable amounts of time spent traveling to and queuing for medical services among poor and rural populations [6], and a scarcity of advanced
medical technology outside central city areas [7]. Wildavsky gives us a discouraging interpretation of the interplay among these problems. Asserting that we cannot "increase quality and quantity of medical services while decreasing costs," [81 he implies that even the most conscientious planning efforts can improve access only by increasing expenditures. Our study represents a more sanguine view of the health crisis. Offering a theoretical approach to health resource allocation and demonstrating linear programming as an appropriate method for its application, the discussion that follows focuses on the computerized tomographic (CT) scanner. The judgments this approach produces with respect to CT scanners recommend it as a highly desirable means of evaluating the issues of health resource allocation that are likely to
Address communications and requests for reprints to Howard P. Greenwald, Research Scientist, Battelle Human Affairs Research Centers, 4000 NE 41st Street, Seattle, WA 98105. John M. Woodward is a consultant at the Health Facilities Corporation in Northbrook, IL. David H. Berg is a consultant at Booz, Allen and Hamilton, Inc. in Chicago. 0017-9124/79/1403-0207/$02.50/0
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confront the next generation of planners. The computerized tomographic scanner has raised more controversy than perhaps any other medical development of the 1970s. The device takes a rapid series of x-rays, pieces them together with the aid of a computer, and displays the output on a fluorescent screen. The resulting image, recorded on magnetic tape for later access, provides the diagnostician with a more accurate and conveniently acquired picture of a patient's internal organs than ever before. With CT scanning, physicians can view internal organs from any angle and obtain pictures of structures of interest at successive depths. The device is particularly useful in diagnosing certain illnesses, when it might otherwise require more risky and painful invasive procedures. CT scanning, for example, allows physicians to view neoplasms and make judgments about the development of tumors without exploratory surgery [9]. The CT scanner has become a rallying point for cost-conscious government officials and consumer advocates because of its high price and rapid proliferation. In 1977, one machine cost between $400,000 and $600,000 for purchase alone; critics charge that many hospitals acquire the machines in the absence of a justifiable demand and pass the high costs of their operation on to all patients. [10] Proliferation of the device has been rapid indeed. Shapiro and Wyman recently described the uncritical impulse of many physicians to "own, operate, exploit, or write about" the device as a contagious pathology of the health care system known as "CAT fever." [111 They urge the development of cost effectiveness measures for the instrumentation, and recommend careful observation and objective testing "by a limited number of institutions (say, 12 to 15) in a collaborative pro-
gram before this technique is widely and uncritically adopted." The insurance industry has joined government in resisting adoption of the new technology; several Blue Cross plans have refused reimbursement for computerized tomography because of the high overall costs incurred by hospitals in providing the new service [12]. The desire for closer regulation of the CT scanner emerges from these concerns. Although regulation is designed to produce more positive results than those hinted at by Wildavsky [8], its effectiveness is limited in practice in important ways. Regulatory agencies seem to have concentrated simply on restricting the deployment of new CT scanners. Moratoria on the acquisition of the devices have been declared in several states, and certificates of need for their purchase are being granted with increasing reluctance nationwide. But while these efforts have commendable goals, they have costly and deleterious consequences if duplicated uncritically in all localities. A more sophisticated approach than "small is beautiful" suggests that there are concrete situations that may require planning strategies other than limitation of new facilities.
A Theory of Health Resource
Allocation Too often, policy makers evaluate specific resources as if the individuals who need them make use of only one at a time, and as though one service has
little to do with any other. While this approach may help identify major problems regarding the availability of single resources, it neglects a very important feature of health care utilization: individuals consume health services in "package" form, typically using several simultaneously or in rapid succession. Patients, for example, frequently make use of physicians and
Transportation or CT Scanners hospital services at the same time; they require surgery, intensive care, and emotional support from professionals in a very rapid succession; they often need followup care, training, or rehabilitation following a hospital stay. Asking whether an appropriate balance of resources exists within a given region, then, is vital. Deciding simply on upper or lower need limits for individual resources neglects the central issue: does the mix of services required for completion of a given procedure meet the combination of needs experienced by the region's residents in the most efficient way?1 Issues of this nature may involve vexing complexities. Planners must decide, for example, which services are actually necessary, and which of the necessary ones take precedence. These decisions often reflect some of the most basic dilemmas of health policy. Of particular significance in the present context is the balance between high technology medicine and support services. The question of what constitutes a proper combination of these two resources has recently become a major issue in the literature of health policy. McKeown, for example, argues that supports which are nontechnical from a medical point of view may be the more effective means of maintaining the lives of many disease sufferers at an acceptable quality [14]. Others caution against too broad an application of this principle, noting, for example, that "a wheelchair is a poor substitute for surgery for the individual needing an arthroplasty of the hip."[15] Obviously, diminishing the supply of high technology medicine too greatly in favor of support services would be a serious policy error. Local planners, though, must address this issue afresh within the unique context of each geographical locale. A simple version of this problem that
may
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might face a local decision maker is the question of whether to allocate the region's resources to install more CT scanners or to promote easier transportation for persons requiring scans. Transportation represents an important type of support service which hospitals occasionally provide in the form of limousines, medicars, and shuttles for transferring patients from one treatment center to another. CT scanners epitomize medical investment of the high technology variety. As clinical evidence has shown, they materially aid diagnosis and treatment of at least some specific ailments. But persons in need of scanning must be able to present themselves physically at hospitals and other diagnostic installations offering the service. Assuming even distribution, the more scanners a region acquires, the less transportation the region's population will require for scanning purposes. Ultimately, the region will have to pay a "bill" for CT scanning which includes more than the cost of purchase, installation, and operation of scanners. The total resources the region expends for scanning will also include transportation to and from scanner installations. This total may include out of pocket costs to patients, contributions of time and resources by friends or relatives who provide transportation, and taxation to support public transportation facilities or subsidies to private carriers. Under the theory of health resource allocation described here, the planner's task is to formulate a strategy which will minimize the size of the entire bill by addressing the full range of resources needed to provide a given service.
The Method of Linear Programming Linear programming (LP), a method applied widely in industry, is a particu-
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larly useful technique for determining the optimal allocation of scarce resources. Industrial decision makers use LP to help solve problems related to transportation and distribution, and to map general production strategies. A firm planning to expand its production capacity, for example, may need to decide between hiring new employees and purchasing new equipment. In such a case, the firm's planners would have to find the least costly mixture of human and material resources. An LP solution to the problem would specify the mixture of investments in labor and machinery that would be the most economical, given certain restrictions such as the minimal volume of production the planners wish to achieve. An LP formulation consists of two main elements: an objective function and a set of constraints. The objective function is a mathematical expression composed of resource variables, terms representing the quantity of each resource in which the planner may choose to invest, and cost coefficients, representing the unit cost of each resource. The constraint set represents the capacity limits of each resource and the minimally acceptable activity level (units produced, persons served, etc.) of the entire system. The mathematics of LP yields an optimal solution that minimizes the objective function within the specified constraints and represents the most economical mixture of resources required to achieve the stated goal. (For a detailed discussion of linear optimization theory and techniques, see Wagner [16].) Directly applicable to investments in the public sector, LP lends itself well to the problem of determining the most appropriate mix of resources needed for adequate CT scanning services in a given geographical area. In this instance, health planners would seek to determine the mixture of investments
in CT scanners and transportation services (or subsidies) which would provide sufficient CT scanning for a regional population at the lowest cost. Scanner costs would include both the initial purchase of the CT scanners and expenses associated with their operation and maintenance. An adequate representation of transportation expenses would include not only the expenses of operating public and private vehicles, but "opportunity costs" for time lost to patients and those attending them while traveling to distant scanning sites. This opportunity cost might reflect patient discomfort and delays in therapeutic measures, as well as time lost from work by patients or individuals accompanying them to CT scanning installations. An LP problem of this kind would include two constraints: 1) demand, in terms of expected utilization of scanning services; and 2) supply, conceived as the scanning capacity of each CT device.
CT Scanners and Transportation in the Chicago Area: An LP Model We expected to find that an LP approach to CT scanning in a particular locality would demonstrate the importance of focusing on a mix of resources rather than considering each resource individually. In order to explore this possibility, we constructed an LP model of CT scanning in a segment of the Chicago metropolitan area which includes the South Side, the southwest suburbs, and adjacent Lake County, Indiana. Encompassing a wide variety of land use and numerous social strata, this region seemed likely to give a good representation of the problems in regional health planning observable in any major metropolitan area. Figure 1 shows Chicago and vicinity and a num-
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FIGURE 1 CHICAGO AND VICINITY SHOWING HEALTH CARE AREAS
Health Care Areas For
Metropolitani Chicago \ (
2 3
4
5
MILES
I
LAKE MICHIGAN
4
10
z z z
17
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ber of "health care areas," subregional districts laid out for a recent planning study. The region covered in the analysis includes districts 1, 4, 5, 10, and 17. The discussion refers to the area encompassed by these five districts as the "South Chicago Region." The Model Like all LP formulations, the model for CT scanning costs in the South Chicago Region includes an objective function and a set of constraints. The objective function takes this form: min , I xij (Tij + Wij) +1 Cyj i
i
i
where resources variables include yj = number of scanners in subregion j, and xii = number of individuals transported to scanners from subregion i to subregion j, or within subregions where i = j (i.e., patients may be transported to scanners within the subregions where they reside or to any of the other four neighboring subregions), and cost coefficients associated with each resource variable, Tij = vehicular cost of transport between subregion i and subregion j, or cost of transportation within subregions where i = j Wij = opportunity cost of patient time expended during transport between subregion i and subregion j, or within subregions where i = j C = costs associated with purchase and operation of CT scanners, identical in all subregions. The model's constraints were a) supply: i xij,syp. (capacity per scanner) for all j; that is, the number of individuals scanned in subregion j cannot exceed the scanner capacity in that region, and
b) demand: I jxij= (expected utilization) for all i; that is, demand for scans in subregion i is estimated by expected utilization levels. Cost Estimates
We used estimates based on American Hospital Association data as cost coefficients for the CT scanner resource variable [17]. Assuming a depreciable life of ten years, the estimated present value of each scanner was $1,509,875. This cost calculation, assuming a discount rate of 10 percent, included Initial investment $500,000 Annual operating costs 23,000 Salaries Maintenance 21,000 120,352 Supplies Total $164,352
Accordingly, the present value of each CT scanner = 10
$500,000 +
$6,5
$164,352
n=(1
+
.10)n
$1,509,875 =
C.
Estimating transportation cost coefficients was more problematical. People live everywhere in the South Chicago Region, and CT scanners may in theory be located anywhere within it. The LP model, however, can incorporate only terms representing finite numbers of trips of determinate lengths. We adopted two strategies to solve this problem. As a proxy for the average trip length between subregions, we calculated the distances between the geographic centers of each subregion. As an approximation of travel distances within subregions, we used the average distance from residents' homes to their
subregion's geographical centers. By estimating distances in this manner, we
Transportation or CT Scanners were able to approximate average travel times within and between subregions. To estimate the cost coefficients for vehicular transportation between and within subregions (Tij), we multiplied the distances determined as described above by the operating costs of the modes of transportation South Chicago residents were likely to use to reach CT scanner installations. We estimated costs for three alternative transportation modes: $2 per mile for critical care vehicles (a likely method for transporting hospitalized persons), $.40 per mile for private autos, and $.10 per mile for public conveyances.2 A fourth cost estimate of $1.00 per mile represents a mix of transport modes used by patients with a variety of injuries and treatment constraints. To estimate the coefficients of the opportunity costs Wij incurred by patients and those attending them, we multiplied average hourly wages for each subregion by average travel times derived as given above. These costs were then combined with vehicular transport costs. The aggregate was projected over a ten-year period and discounted at a rate of 10 percent to reflect the present value of total transportation and opportunity costs. Constraints The relative novelty of CT scanning introduces an element of guesswork into any estimation of supply and demand. All planning efforts, though, require estimates of these constraints. For the LP analysis, we estimate supply and demand constraints according to the most accurate information available to actual health planners in the South Chicago Region. In this manner, we fixed the maximum output capacity of individual CT scanners (the supply constraint) at 4,000 scans per year.3 Demand for CT scanning is also uncertain. Sweden, a country where gener-
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ous public funding has resulted in nearly universal access to health care, reports that 2 individuals per thousand receive CT scans per year [17, p. 71]. Because utilization of CT scanning seems likely to increase as physicians become more aware of its applicability, we regarded the Swedish figure as low, and considered estimates of 7, 15, and 25 per thousand as alternative demand constraints in the analysis.
Findings Using the numerical estimates described above for cost coefficients and constraints, we performed a series of LP runs to determine the costs of providing ten years of CT scanning to the South Chicago Region under various resource allocation and scanner deployment strategies. By allowing LP computer routines to determine the magnitudes of resource variables in the objective function, we were able to estimate the minimum cost of CT scanning under alternative estimates of transportation costs and scanner capacity. In a second stage of the analysis, we further constrained the LP to produce integer solutions which gave more pragmatic results. This step allowed us to perform a series of comparisons of realistic deployment strategies in order to evaluate the costs of each option. Table 1 presents the total costs of CT scanning in the South Chicago Region under alternative estimates of transportation costs and utilization levels. The values given in the table represent minimum total costs for ten years of CT scanning under each pair of utilization level and transportation cost assumptions. The opportunity cost of patient and attendant time expended during transport was included in each utilization-transportation alternative. We adopted the utilization level estimate of seven scans per thousand
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Table 1: Minimum Cost (Millions of Dollars) of CT Scanning in the South Chicago Region under Various Cost and Utilization Assumptions* Utilization Level (scans per 1,000 population)
Transportation Costs (dollars per mile) .10
.40
1.00
2.00 4.7 16.4
2
3.0
7
10.5
3.3 11.4
15
22.4 37.3
24.4
28.4
35.2
40.6
47.7
58.6
25
3.8
13.3
* Figures in table represent costs of systems utilizing optimally placed CT scanners over a 10-year period. Factors reflecting the opportunity cost of patient and attendant time were included in these calculations.
population and the transportation cost estimate of $1 per mile as the basis for a more detailed analysis, while applying the same assumption with regard to the opportunity cost of travel time used in previous analyses. These figures, which gave rise to an estimated optimal cost for CT scanning of $13.3 million, appeared to reflect conditions in the South Chicago Region most accurately. The Chicago Health Systems Agency's review criteria suggest that CT scanner utilization in excess of eight scans per thousand population should indicate a need for additional scanner capacity in the service area [19]. The figure of $1 per mile for transportation represents a weighted mix of transportation services reflecting the use of transportation services of varying medical and cost intensity: many of the individuals presently receiving CT scans are hospitalized and require specially equipped medical vehicles for transportation to other facilities, while ambulatory patients require less specialized and expensive transportation services.
Table 2 illustrates several strategies available to planners for use in designing a regional CT scanner setup under these cost and utilization-level assumptions. The first column in Table 2 reflects the deployment of CT scanners in the South Chicago Region required under the optimal solution. Unfortunately, the figure of $13.3 million associated with this solution cannot be implemented. In order to provide ten years of scanning for the South Chicago Region's population at this price, fractions of scanners would have to be placed in each district; a total of 5.75 scanners would be required. While these figures are meaningful in mathematical terms, they fail to offer concrete guidelines to planners who may deploy only whole machines. Actual decision makers, then, must formulate a strategy which approximates this solution as closely as possible. The optimal (noninteger) solution in Table 2 seems to suggest that planners faced with real deployment decisions would do best to deny a scanner to District 5-the area where, according to the optimal solution, the smallest "fraction" of a scanner is needed-and transport residents of District 5 to other districts when they needed CT scans. A good integer approximation of the optimal solution, then, appears to be Solution A (see Table 2). According to this solution, a total of six CT scanners would be needed: two in District 1, two in District 4, one apiece in Districts 10 and 17, and none in District 5. The total ten-year cost of this strategy would be $15.3 million, about 15 percent higher than the optimal (but impracticable) solution. The higher cost of this solution results from additional movement of patients from one district to another and purchase of additional scanning capacity. Solutions B and C constitute more costly strategies. Both represent ineffi-
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Table 2: Cost of CT Scaing in the South Chicago Region under Various Deployment Strategies Ditrict No.
Optimal Solution
A
Feasible (Integer) Solutions C B
D
Actual Deployment
1 4 5 10 17 Total CT Scanners
1.65* 1.68 .62 .96 .84
2 2 0 1 1
2 2 1 0 1
2 2 1 1 0
2 2 1 1 1
4 1 0 1 2
5.75
6
6
6
7
8
Total Cost (millions)
$13.3t
$15.3
$21.4
$22.9
$15.2
$21.1*
* Figures to the right of district numbers represent the number of CT scanners allocated to each LP solution. tBottom line figures represent cost over 10-year period. *Total cost estimates for 10 years of scanning under present scanner deployment assume conditions and costs included in model.
cient resource allocation. As in Solution A, both call for a total of six scanners, and require the movement of patients from a district without a scanner to other districts with scanners. Total costs of Solutions B and C, though, are considerably higher than the cost of Solution A. The expenditures of $21.4 and $22.9 million for these strategies are about 45 percent greater than those for Solution A. However, the higher costs of these solutions derive from higher transportation costs rather than from the cost of providing greater scanning capacity. All three solutions supply precisely equal amounts of scanners and scanning capacity. Solution D represents the best practicable strategy. As Table 2 indicates, this strategy provides ten years of CT scanning to South Chicago residents at a cost of $15.2 million. The total cost of Solution D is slightly less than that of Solution A and considerably less than the costs of Solutions B and C. A striking feature of Solution D is that it calls for seven scanners, while the more expensive strategies call for six. Under
the assumption of this analysis, the high cost of purchasing and maintaining an additional CT scanner in the South Chicago Region does not outweigh the benefits realized by cutting down on the expenses related to transportation. Common to all integer solutions to the problem is the provision of excess scanning capacity. As indicated in Table 3, regional excess capacity of 1,040 scans is provided in the three solutions with six scanners, while the potential to perform 5,040 additional scans is provided by the seven-scanner option. Among Solutions A, B, and C, differences in location of excess capacity reflect the influences of transportation and opportunity costs in determining scanner utilization. Although Solution D, the seven-scanner option, generates the greatest excess capacity, it is the least expensive of the four solutions. Consideration of the cost of all resources needed to deliver CT scanning services reveals that excess capacity of a single resource does not necessarily imply inefficient
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Table 3: Excess CT Scanner Capacity in the South Chicago Region Under Various Deployment Strategies* District No.
Optimal Solution
A
1 4 5 10 17 Total Excess in Region
0 0 0 0 0
0 236 0 164 640
1,040 0 0 0 0
0
1,040
1,040
Feasible (Integer) Solutions C B
Actual
D
Deploymentt
1,040 0 0 0 0
1,406 1,294 1,536 164 640
4,236 0 0 164 4,640
1,040
5,040
9,040
Figures in table represent excess capacity per year. tExcess capacity of scanners currently deployed assumes conditions stated in model. *
delivery of the service. The decline in total costs in Solution D reflects increased capital expenditures offset by decreased transportation and opportunity costs. Accounting for the cost of individual elements comprising the package of resources needed to deliver CT scanning services uncovers important economic trade-offs which should be considered in making resource allocation decisions. It is clear that, by providing too few CT scanners, planners may increase costs beyond what they need to be. But if Solution A, by denying a CT scanner to District 5, represents an error in health resource allocation, Solutions B and C would be far more serious mistakes. Even though B and C require fewer expensive machines than D, they cost considerably more. Although they require no more scanners than A, they are a great deal more expensive. The difference between an economical and a wasteful strategy appears to depend more heavily on siting of CT scanners than on unilateral restriction of their numbers. In view of the controversy over CT scanners, a comparison of the strategies explored above with the actual deployment pattern in the South Chicago
Region seemed indispensable to our study. We constrained the program to produce a minimum value of the objective function with four CT scanners in District 1, one in District 4, none in District 5, one in District 10, and two in District 17. According to the region's Health Systems Agencies, this was the actual number of CT scanners in each district in 1977. The rightmost column of Tables 2 and 3 present the cost and excess capacity conditions of this eightunit system under the assumptions of our LP model. The cost of this system, $21.1 million over ten years, is much higher than those of Solutions A and D, but slightly lower than the costs of B and C. Although factors which we omitted from our analysis may account for some of the differences in cost between Solution D and the actual deployment pattern, it seems likely that at least some cost saving could have resulted from a planning effort aimed at optimal siting.
Discussion The theory and method of health resource allocation discussed in this paper illustrate the importance of viewing each offering of the health care sys-
Transportation or CT Scanners tem as a package of interrelated resources. An exclusive focus on the capacity and utilization of CT scanners in the South Chicago Region would overlook the part transportation plays in determining the total bill for CT scanning. By asking only whether their regions possess sufficient numbers of scanners to process all residents in need, decision makers in other localities might formulate deployment strategies that would be much more expensive than they need to be. Truly effective planning approaches would incorporate an understanding that costs of transportation-whether paid by government or the consumer-could exceed the cost of additional CT scanners. The option of deploying additional scanners would be especially attractive in localities where residents have to travel long distances or utilize inconvenient and expensive means of transportation to reach existing facilities. Readers should understand that an application of this method in other settings should include a careful review of cost coefficients, as well as demand and capacity constraints. The rapid changes in costs of both scanning and transportation need to be accounted for, as well as regional variations in those costs. Additional types of costs may also be included as a refinement of this approach: costs associated with physician travel and inconvenience, scheduling costs, and greater quantification of opportunity costs are
possible examples. Attention should also be focused on the determination of travel times, because they underlie the computed magnitude of all transportation costs. The definition of subregional boundaries is of particular concern. Use of an average distance approach as applied in this study expresses distance as a function of regional boundaries. As such, distances and travel time may vary accord-
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ing to the selection of geographical regions used in the analysis. Capacity and demand constraints should also undergo reevaluation in future applications. Capacity of individual scanners is sensitive to ongoing technological development and the pattern of the learning and experience curve attending to operation of the equipment. Demand for future scanning services may also be expected to vary. Refinement of techniques and further technological developments will contribute to an evolution of the mix of cases that reap the greatest benefit from the equipment. Future trends in regulation, reimbursement, and consumer awareness also affect demand for the service. The breadth of existing health care legislation and the present structure of the health care industry present additional difficulties for the concrete application of this article's perspective. Planners in Health Systems Agencies, for example, now possess a mandate simply to limit new development. Current legislation enables them to limit the number of CT scanners in their localities, but not to determine where they are to be located. As our analysis indicates, limitations placed on the acquisition of new facilities in a given service region may not necessarily promote cost containment. Smaller numbers of facilities are quite compatible with higher costs. Additional problems arise from the fact that CT scanner deployment has already been quite extensive. While regulatory agencies may declare moritoria on purchases of CT scanners, they may not order the removal or relocation of existing facilities. The value of this discussion to planners and policy makers is largely as an approach to future developments. In an age of high technology medicine, it is inevitable that newer, more powerful, and more expensive devices and proce-
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dures will appear on the market in the closer coordination with health care years to come. Just as inevitable will be providers to make concrete use of the a continuation of the demand among theory and method we have proposed political figures and consumer advo- here. cates for better, more comprehensive delivery of services. To respond effectively to such demand, planners will ACKNOWLEDGEMENTS have to stay alert to new technological The authors wish to thank Michael J. developments before they are implemented by individual health care pro- Donnelly for important contributions viders, determine the set of needs that to the initial stages of this research and accompanies each high technology Richard W. Foster for useful comments offering, and make judgments about the on an earlier draft. Cindy Ostroff denecessary number of installations and serves special thanks for preparing the their optimal sitings in advance. graphic presentation. Clearly, planners will need to establish END NOTES 'The importance of providing a proper mix of services receives strong emphasis, for example, in the context of chronic disease. See Yelin et al. [13]. Yelin and his associates note that the availability of social services can lower utilization of medical services by helping chronic disease sufferers cope with their illnesses. Similarly, adequate medical care can reduce demand for social support services. The authors imply strongly that the proper combination o'f medical and social services is necessary to provide chronic disease patients with the most appropriate care at lowest cost. 2The estimate for critical care vehicles reflected the Chicago Fire Department's experience with mobile intensive care ambulance services. Costs were derived as follows: annual depreciation, $8,000; annual paramedic salaries, $30,000; maintenance/equipment replacement, $6,000; administrative overhead, $6,000; estimated total annual operating expenses, $50,000; average annual mileage, $25,000; and estimated cost per mile, $2.00. Cost estimates for the operation of private autos ($.40 per mile) and mass transportation ($.10 per mile) were derived similarly from estimated prevailing costs in the area. 3Federal planning guidelines released in September 1977 suggest an upper annual utilization limit of 4,000 scans. See [18]. Although recent planning guidelines cite 2,500 scans per year as a minimum level of utilization, 4,000 scans was considered an appropriate upper limit. Use of a capacity constraint approximating upper operating limits, as opposed to acceptable minimum levels of operation, simulates capital expenditures at more realistic levels. Moreover, low capacity will lead to more rapid achievement of capacity at a particular site requiring additional use of transportation services. Use of a higher capacity constraint is more conservative with respect to the overall level of expenditures generated. REFERENCES 1. Hyman, H.H. Health
Planning: A Systematic Approach, p. 38. Germantown, MD:
Aspen Systems Corporation, 1976.
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2 O'Connor, J.T. Comprehensive health planning: Dreams and realities. Health and Society 52:397, Fall 1974 3. Inglehart, J.K. The cost and regulation of medical technology: Future policy directions. Health and Society 55:36, Winter 1977. 4. Warner, K.E. Treatment decision making in catastrophic illness. Medical Care 15:21, Jan. 1977. 5. Terris, M. The need for a national health program. Bulletin of the New York Academy of Medicine 18:73, Jan. 1972. 6. Aday, L.A. and R. Andersen. Access to Medical Care, p. 73. Ann Arbor: Health Admin-
istration Press, 1975. 7. Tarlov, A.R., B. Schwartz, and H.P. Greenwald. Innovation in regional health care: The academic medical center's prospects and problems. Working paper, University of Chi-
cago, 1978. 8. Wildavsky, A. Can Health Care Be Planned? 1976 Michael Davis Lecture, p. 8. Chicago: Center for Health Administration Studies, 1976. 9. Rockoff, S.D. The evolving role of computerized tomography in radiation oncology. Cancer 39(2):694, Feb. 1977. 10. Schwartz, H. The government puts a damper on the scanner bonanza. New York Times,
Dec. 8, 1977. 11. Shapiro, S.H. and S.M. Wyman. CAT fever. New England lournal of Medicine 294:954,
Apr. 22, 1976. 12. Phillips, D.F. and K. Lillie. Putting the leash on the CAT. Hospitals 50:45, July 1, 1976. 13. Yelin, E.H. et al. Social problems, services, and policy for persons with rheumatoid arthritis. Social Science and Medicine, in press. 14. McKeown, T. The Role of Medicine: Dream, Mirage or Nemesis? London: Nuffield Provincial Hospitals Trust, 1976. 15. Godber, G.E. McKeown's "The Role of Medicine": Comments from a former chief medical officer. Health and Society 55:376, Summer 1977. 16. Wagner, H.M. Principles of Management Science. Englewood Cliffs, NJ: Prentice-Hall, 1970. 17. American Hospital Association. CT Scanners: A Technical Report. Chicago: American Hospital Association, 1977. 18. National guidelines for health planning: Advance notice of proposed rolemaking. Federal Register 42(185):48, 505, Sept. 23, 1977. 19. Chicago Health Systems Agency, Inc. Project and Program Review Manual: Procedures and Criteria, 1978-1979. Chicago: Chicago Health Systems Agency, Inc., 1978.
Two central issues have emerged from the furor over health policy: cost containment and access to quality care. Commentaries on the "health crisis" almost invariably commence with a discussion of costs. They cite figures to illustrate the seemingly malignant domination by health services of ever greater portions of the gross national product [1] and decry the breakdown of the market's capacity to serve as an effective immunological mechanism against this process [2-41. Those concerned with access-access not merely to health professionals and facilities, but to the most appropriate forms of care-report inadequate numbers of physicians in needed specialties [5], unreasonable amounts of time spent traveling to and queuing for medical services among poor and rural populations [6], and a scarcity of advanced
medical technology outside central city areas [7]. Wildavsky gives us a discouraging interpretation of the interplay among these problems. Asserting that we cannot "increase quality and quantity of medical services while decreasing costs," [81 he implies that even the most conscientious planning efforts can improve access only by increasing expenditures. Our study represents a more sanguine view of the health crisis. Offering a theoretical approach to health resource allocation and demonstrating linear programming as an appropriate method for its application, the discussion that follows focuses on the computerized tomographic (CT) scanner. The judgments this approach produces with respect to CT scanners recommend it as a highly desirable means of evaluating the issues of health resource allocation that are likely to
Address communications and requests for reprints to Howard P. Greenwald, Research Scientist, Battelle Human Affairs Research Centers, 4000 NE 41st Street, Seattle, WA 98105. John M. Woodward is a consultant at the Health Facilities Corporation in Northbrook, IL. David H. Berg is a consultant at Booz, Allen and Hamilton, Inc. in Chicago. 0017-9124/79/1403-0207/$02.50/0
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confront the next generation of planners. The computerized tomographic scanner has raised more controversy than perhaps any other medical development of the 1970s. The device takes a rapid series of x-rays, pieces them together with the aid of a computer, and displays the output on a fluorescent screen. The resulting image, recorded on magnetic tape for later access, provides the diagnostician with a more accurate and conveniently acquired picture of a patient's internal organs than ever before. With CT scanning, physicians can view internal organs from any angle and obtain pictures of structures of interest at successive depths. The device is particularly useful in diagnosing certain illnesses, when it might otherwise require more risky and painful invasive procedures. CT scanning, for example, allows physicians to view neoplasms and make judgments about the development of tumors without exploratory surgery [9]. The CT scanner has become a rallying point for cost-conscious government officials and consumer advocates because of its high price and rapid proliferation. In 1977, one machine cost between $400,000 and $600,000 for purchase alone; critics charge that many hospitals acquire the machines in the absence of a justifiable demand and pass the high costs of their operation on to all patients. [10] Proliferation of the device has been rapid indeed. Shapiro and Wyman recently described the uncritical impulse of many physicians to "own, operate, exploit, or write about" the device as a contagious pathology of the health care system known as "CAT fever." [111 They urge the development of cost effectiveness measures for the instrumentation, and recommend careful observation and objective testing "by a limited number of institutions (say, 12 to 15) in a collaborative pro-
gram before this technique is widely and uncritically adopted." The insurance industry has joined government in resisting adoption of the new technology; several Blue Cross plans have refused reimbursement for computerized tomography because of the high overall costs incurred by hospitals in providing the new service [12]. The desire for closer regulation of the CT scanner emerges from these concerns. Although regulation is designed to produce more positive results than those hinted at by Wildavsky [8], its effectiveness is limited in practice in important ways. Regulatory agencies seem to have concentrated simply on restricting the deployment of new CT scanners. Moratoria on the acquisition of the devices have been declared in several states, and certificates of need for their purchase are being granted with increasing reluctance nationwide. But while these efforts have commendable goals, they have costly and deleterious consequences if duplicated uncritically in all localities. A more sophisticated approach than "small is beautiful" suggests that there are concrete situations that may require planning strategies other than limitation of new facilities.
A Theory of Health Resource
Allocation Too often, policy makers evaluate specific resources as if the individuals who need them make use of only one at a time, and as though one service has
little to do with any other. While this approach may help identify major problems regarding the availability of single resources, it neglects a very important feature of health care utilization: individuals consume health services in "package" form, typically using several simultaneously or in rapid succession. Patients, for example, frequently make use of physicians and
Transportation or CT Scanners hospital services at the same time; they require surgery, intensive care, and emotional support from professionals in a very rapid succession; they often need followup care, training, or rehabilitation following a hospital stay. Asking whether an appropriate balance of resources exists within a given region, then, is vital. Deciding simply on upper or lower need limits for individual resources neglects the central issue: does the mix of services required for completion of a given procedure meet the combination of needs experienced by the region's residents in the most efficient way?1 Issues of this nature may involve vexing complexities. Planners must decide, for example, which services are actually necessary, and which of the necessary ones take precedence. These decisions often reflect some of the most basic dilemmas of health policy. Of particular significance in the present context is the balance between high technology medicine and support services. The question of what constitutes a proper combination of these two resources has recently become a major issue in the literature of health policy. McKeown, for example, argues that supports which are nontechnical from a medical point of view may be the more effective means of maintaining the lives of many disease sufferers at an acceptable quality [14]. Others caution against too broad an application of this principle, noting, for example, that "a wheelchair is a poor substitute for surgery for the individual needing an arthroplasty of the hip."[15] Obviously, diminishing the supply of high technology medicine too greatly in favor of support services would be a serious policy error. Local planners, though, must address this issue afresh within the unique context of each geographical locale. A simple version of this problem that
may
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might face a local decision maker is the question of whether to allocate the region's resources to install more CT scanners or to promote easier transportation for persons requiring scans. Transportation represents an important type of support service which hospitals occasionally provide in the form of limousines, medicars, and shuttles for transferring patients from one treatment center to another. CT scanners epitomize medical investment of the high technology variety. As clinical evidence has shown, they materially aid diagnosis and treatment of at least some specific ailments. But persons in need of scanning must be able to present themselves physically at hospitals and other diagnostic installations offering the service. Assuming even distribution, the more scanners a region acquires, the less transportation the region's population will require for scanning purposes. Ultimately, the region will have to pay a "bill" for CT scanning which includes more than the cost of purchase, installation, and operation of scanners. The total resources the region expends for scanning will also include transportation to and from scanner installations. This total may include out of pocket costs to patients, contributions of time and resources by friends or relatives who provide transportation, and taxation to support public transportation facilities or subsidies to private carriers. Under the theory of health resource allocation described here, the planner's task is to formulate a strategy which will minimize the size of the entire bill by addressing the full range of resources needed to provide a given service.
The Method of Linear Programming Linear programming (LP), a method applied widely in industry, is a particu-
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larly useful technique for determining the optimal allocation of scarce resources. Industrial decision makers use LP to help solve problems related to transportation and distribution, and to map general production strategies. A firm planning to expand its production capacity, for example, may need to decide between hiring new employees and purchasing new equipment. In such a case, the firm's planners would have to find the least costly mixture of human and material resources. An LP solution to the problem would specify the mixture of investments in labor and machinery that would be the most economical, given certain restrictions such as the minimal volume of production the planners wish to achieve. An LP formulation consists of two main elements: an objective function and a set of constraints. The objective function is a mathematical expression composed of resource variables, terms representing the quantity of each resource in which the planner may choose to invest, and cost coefficients, representing the unit cost of each resource. The constraint set represents the capacity limits of each resource and the minimally acceptable activity level (units produced, persons served, etc.) of the entire system. The mathematics of LP yields an optimal solution that minimizes the objective function within the specified constraints and represents the most economical mixture of resources required to achieve the stated goal. (For a detailed discussion of linear optimization theory and techniques, see Wagner [16].) Directly applicable to investments in the public sector, LP lends itself well to the problem of determining the most appropriate mix of resources needed for adequate CT scanning services in a given geographical area. In this instance, health planners would seek to determine the mixture of investments
in CT scanners and transportation services (or subsidies) which would provide sufficient CT scanning for a regional population at the lowest cost. Scanner costs would include both the initial purchase of the CT scanners and expenses associated with their operation and maintenance. An adequate representation of transportation expenses would include not only the expenses of operating public and private vehicles, but "opportunity costs" for time lost to patients and those attending them while traveling to distant scanning sites. This opportunity cost might reflect patient discomfort and delays in therapeutic measures, as well as time lost from work by patients or individuals accompanying them to CT scanning installations. An LP problem of this kind would include two constraints: 1) demand, in terms of expected utilization of scanning services; and 2) supply, conceived as the scanning capacity of each CT device.
CT Scanners and Transportation in the Chicago Area: An LP Model We expected to find that an LP approach to CT scanning in a particular locality would demonstrate the importance of focusing on a mix of resources rather than considering each resource individually. In order to explore this possibility, we constructed an LP model of CT scanning in a segment of the Chicago metropolitan area which includes the South Side, the southwest suburbs, and adjacent Lake County, Indiana. Encompassing a wide variety of land use and numerous social strata, this region seemed likely to give a good representation of the problems in regional health planning observable in any major metropolitan area. Figure 1 shows Chicago and vicinity and a num-
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211
FIGURE 1 CHICAGO AND VICINITY SHOWING HEALTH CARE AREAS
Health Care Areas For
Metropolitani Chicago \ (
2 3
4
5
MILES
I
LAKE MICHIGAN
4
10
z z z
17
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ber of "health care areas," subregional districts laid out for a recent planning study. The region covered in the analysis includes districts 1, 4, 5, 10, and 17. The discussion refers to the area encompassed by these five districts as the "South Chicago Region." The Model Like all LP formulations, the model for CT scanning costs in the South Chicago Region includes an objective function and a set of constraints. The objective function takes this form: min , I xij (Tij + Wij) +1 Cyj i
i
i
where resources variables include yj = number of scanners in subregion j, and xii = number of individuals transported to scanners from subregion i to subregion j, or within subregions where i = j (i.e., patients may be transported to scanners within the subregions where they reside or to any of the other four neighboring subregions), and cost coefficients associated with each resource variable, Tij = vehicular cost of transport between subregion i and subregion j, or cost of transportation within subregions where i = j Wij = opportunity cost of patient time expended during transport between subregion i and subregion j, or within subregions where i = j C = costs associated with purchase and operation of CT scanners, identical in all subregions. The model's constraints were a) supply: i xij,syp. (capacity per scanner) for all j; that is, the number of individuals scanned in subregion j cannot exceed the scanner capacity in that region, and
b) demand: I jxij= (expected utilization) for all i; that is, demand for scans in subregion i is estimated by expected utilization levels. Cost Estimates
We used estimates based on American Hospital Association data as cost coefficients for the CT scanner resource variable [17]. Assuming a depreciable life of ten years, the estimated present value of each scanner was $1,509,875. This cost calculation, assuming a discount rate of 10 percent, included Initial investment $500,000 Annual operating costs 23,000 Salaries Maintenance 21,000 120,352 Supplies Total $164,352
Accordingly, the present value of each CT scanner = 10
$500,000 +
$6,5
$164,352
n=(1
+
.10)n
$1,509,875 =
C.
Estimating transportation cost coefficients was more problematical. People live everywhere in the South Chicago Region, and CT scanners may in theory be located anywhere within it. The LP model, however, can incorporate only terms representing finite numbers of trips of determinate lengths. We adopted two strategies to solve this problem. As a proxy for the average trip length between subregions, we calculated the distances between the geographic centers of each subregion. As an approximation of travel distances within subregions, we used the average distance from residents' homes to their
subregion's geographical centers. By estimating distances in this manner, we
Transportation or CT Scanners were able to approximate average travel times within and between subregions. To estimate the cost coefficients for vehicular transportation between and within subregions (Tij), we multiplied the distances determined as described above by the operating costs of the modes of transportation South Chicago residents were likely to use to reach CT scanner installations. We estimated costs for three alternative transportation modes: $2 per mile for critical care vehicles (a likely method for transporting hospitalized persons), $.40 per mile for private autos, and $.10 per mile for public conveyances.2 A fourth cost estimate of $1.00 per mile represents a mix of transport modes used by patients with a variety of injuries and treatment constraints. To estimate the coefficients of the opportunity costs Wij incurred by patients and those attending them, we multiplied average hourly wages for each subregion by average travel times derived as given above. These costs were then combined with vehicular transport costs. The aggregate was projected over a ten-year period and discounted at a rate of 10 percent to reflect the present value of total transportation and opportunity costs. Constraints The relative novelty of CT scanning introduces an element of guesswork into any estimation of supply and demand. All planning efforts, though, require estimates of these constraints. For the LP analysis, we estimate supply and demand constraints according to the most accurate information available to actual health planners in the South Chicago Region. In this manner, we fixed the maximum output capacity of individual CT scanners (the supply constraint) at 4,000 scans per year.3 Demand for CT scanning is also uncertain. Sweden, a country where gener-
213
ous public funding has resulted in nearly universal access to health care, reports that 2 individuals per thousand receive CT scans per year [17, p. 71]. Because utilization of CT scanning seems likely to increase as physicians become more aware of its applicability, we regarded the Swedish figure as low, and considered estimates of 7, 15, and 25 per thousand as alternative demand constraints in the analysis.
Findings Using the numerical estimates described above for cost coefficients and constraints, we performed a series of LP runs to determine the costs of providing ten years of CT scanning to the South Chicago Region under various resource allocation and scanner deployment strategies. By allowing LP computer routines to determine the magnitudes of resource variables in the objective function, we were able to estimate the minimum cost of CT scanning under alternative estimates of transportation costs and scanner capacity. In a second stage of the analysis, we further constrained the LP to produce integer solutions which gave more pragmatic results. This step allowed us to perform a series of comparisons of realistic deployment strategies in order to evaluate the costs of each option. Table 1 presents the total costs of CT scanning in the South Chicago Region under alternative estimates of transportation costs and utilization levels. The values given in the table represent minimum total costs for ten years of CT scanning under each pair of utilization level and transportation cost assumptions. The opportunity cost of patient and attendant time expended during transport was included in each utilization-transportation alternative. We adopted the utilization level estimate of seven scans per thousand
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Table 1: Minimum Cost (Millions of Dollars) of CT Scanning in the South Chicago Region under Various Cost and Utilization Assumptions* Utilization Level (scans per 1,000 population)
Transportation Costs (dollars per mile) .10
.40
1.00
2.00 4.7 16.4
2
3.0
7
10.5
3.3 11.4
15
22.4 37.3
24.4
28.4
35.2
40.6
47.7
58.6
25
3.8
13.3
* Figures in table represent costs of systems utilizing optimally placed CT scanners over a 10-year period. Factors reflecting the opportunity cost of patient and attendant time were included in these calculations.
population and the transportation cost estimate of $1 per mile as the basis for a more detailed analysis, while applying the same assumption with regard to the opportunity cost of travel time used in previous analyses. These figures, which gave rise to an estimated optimal cost for CT scanning of $13.3 million, appeared to reflect conditions in the South Chicago Region most accurately. The Chicago Health Systems Agency's review criteria suggest that CT scanner utilization in excess of eight scans per thousand population should indicate a need for additional scanner capacity in the service area [19]. The figure of $1 per mile for transportation represents a weighted mix of transportation services reflecting the use of transportation services of varying medical and cost intensity: many of the individuals presently receiving CT scans are hospitalized and require specially equipped medical vehicles for transportation to other facilities, while ambulatory patients require less specialized and expensive transportation services.
Table 2 illustrates several strategies available to planners for use in designing a regional CT scanner setup under these cost and utilization-level assumptions. The first column in Table 2 reflects the deployment of CT scanners in the South Chicago Region required under the optimal solution. Unfortunately, the figure of $13.3 million associated with this solution cannot be implemented. In order to provide ten years of scanning for the South Chicago Region's population at this price, fractions of scanners would have to be placed in each district; a total of 5.75 scanners would be required. While these figures are meaningful in mathematical terms, they fail to offer concrete guidelines to planners who may deploy only whole machines. Actual decision makers, then, must formulate a strategy which approximates this solution as closely as possible. The optimal (noninteger) solution in Table 2 seems to suggest that planners faced with real deployment decisions would do best to deny a scanner to District 5-the area where, according to the optimal solution, the smallest "fraction" of a scanner is needed-and transport residents of District 5 to other districts when they needed CT scans. A good integer approximation of the optimal solution, then, appears to be Solution A (see Table 2). According to this solution, a total of six CT scanners would be needed: two in District 1, two in District 4, one apiece in Districts 10 and 17, and none in District 5. The total ten-year cost of this strategy would be $15.3 million, about 15 percent higher than the optimal (but impracticable) solution. The higher cost of this solution results from additional movement of patients from one district to another and purchase of additional scanning capacity. Solutions B and C constitute more costly strategies. Both represent ineffi-
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Table 2: Cost of CT Scaing in the South Chicago Region under Various Deployment Strategies Ditrict No.
Optimal Solution
A
Feasible (Integer) Solutions C B
D
Actual Deployment
1 4 5 10 17 Total CT Scanners
1.65* 1.68 .62 .96 .84
2 2 0 1 1
2 2 1 0 1
2 2 1 1 0
2 2 1 1 1
4 1 0 1 2
5.75
6
6
6
7
8
Total Cost (millions)
$13.3t
$15.3
$21.4
$22.9
$15.2
$21.1*
* Figures to the right of district numbers represent the number of CT scanners allocated to each LP solution. tBottom line figures represent cost over 10-year period. *Total cost estimates for 10 years of scanning under present scanner deployment assume conditions and costs included in model.
cient resource allocation. As in Solution A, both call for a total of six scanners, and require the movement of patients from a district without a scanner to other districts with scanners. Total costs of Solutions B and C, though, are considerably higher than the cost of Solution A. The expenditures of $21.4 and $22.9 million for these strategies are about 45 percent greater than those for Solution A. However, the higher costs of these solutions derive from higher transportation costs rather than from the cost of providing greater scanning capacity. All three solutions supply precisely equal amounts of scanners and scanning capacity. Solution D represents the best practicable strategy. As Table 2 indicates, this strategy provides ten years of CT scanning to South Chicago residents at a cost of $15.2 million. The total cost of Solution D is slightly less than that of Solution A and considerably less than the costs of Solutions B and C. A striking feature of Solution D is that it calls for seven scanners, while the more expensive strategies call for six. Under
the assumption of this analysis, the high cost of purchasing and maintaining an additional CT scanner in the South Chicago Region does not outweigh the benefits realized by cutting down on the expenses related to transportation. Common to all integer solutions to the problem is the provision of excess scanning capacity. As indicated in Table 3, regional excess capacity of 1,040 scans is provided in the three solutions with six scanners, while the potential to perform 5,040 additional scans is provided by the seven-scanner option. Among Solutions A, B, and C, differences in location of excess capacity reflect the influences of transportation and opportunity costs in determining scanner utilization. Although Solution D, the seven-scanner option, generates the greatest excess capacity, it is the least expensive of the four solutions. Consideration of the cost of all resources needed to deliver CT scanning services reveals that excess capacity of a single resource does not necessarily imply inefficient
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Table 3: Excess CT Scanner Capacity in the South Chicago Region Under Various Deployment Strategies* District No.
Optimal Solution
A
1 4 5 10 17 Total Excess in Region
0 0 0 0 0
0 236 0 164 640
1,040 0 0 0 0
0
1,040
1,040
Feasible (Integer) Solutions C B
Actual
D
Deploymentt
1,040 0 0 0 0
1,406 1,294 1,536 164 640
4,236 0 0 164 4,640
1,040
5,040
9,040
Figures in table represent excess capacity per year. tExcess capacity of scanners currently deployed assumes conditions stated in model. *
delivery of the service. The decline in total costs in Solution D reflects increased capital expenditures offset by decreased transportation and opportunity costs. Accounting for the cost of individual elements comprising the package of resources needed to deliver CT scanning services uncovers important economic trade-offs which should be considered in making resource allocation decisions. It is clear that, by providing too few CT scanners, planners may increase costs beyond what they need to be. But if Solution A, by denying a CT scanner to District 5, represents an error in health resource allocation, Solutions B and C would be far more serious mistakes. Even though B and C require fewer expensive machines than D, they cost considerably more. Although they require no more scanners than A, they are a great deal more expensive. The difference between an economical and a wasteful strategy appears to depend more heavily on siting of CT scanners than on unilateral restriction of their numbers. In view of the controversy over CT scanners, a comparison of the strategies explored above with the actual deployment pattern in the South Chicago
Region seemed indispensable to our study. We constrained the program to produce a minimum value of the objective function with four CT scanners in District 1, one in District 4, none in District 5, one in District 10, and two in District 17. According to the region's Health Systems Agencies, this was the actual number of CT scanners in each district in 1977. The rightmost column of Tables 2 and 3 present the cost and excess capacity conditions of this eightunit system under the assumptions of our LP model. The cost of this system, $21.1 million over ten years, is much higher than those of Solutions A and D, but slightly lower than the costs of B and C. Although factors which we omitted from our analysis may account for some of the differences in cost between Solution D and the actual deployment pattern, it seems likely that at least some cost saving could have resulted from a planning effort aimed at optimal siting.
Discussion The theory and method of health resource allocation discussed in this paper illustrate the importance of viewing each offering of the health care sys-
Transportation or CT Scanners tem as a package of interrelated resources. An exclusive focus on the capacity and utilization of CT scanners in the South Chicago Region would overlook the part transportation plays in determining the total bill for CT scanning. By asking only whether their regions possess sufficient numbers of scanners to process all residents in need, decision makers in other localities might formulate deployment strategies that would be much more expensive than they need to be. Truly effective planning approaches would incorporate an understanding that costs of transportation-whether paid by government or the consumer-could exceed the cost of additional CT scanners. The option of deploying additional scanners would be especially attractive in localities where residents have to travel long distances or utilize inconvenient and expensive means of transportation to reach existing facilities. Readers should understand that an application of this method in other settings should include a careful review of cost coefficients, as well as demand and capacity constraints. The rapid changes in costs of both scanning and transportation need to be accounted for, as well as regional variations in those costs. Additional types of costs may also be included as a refinement of this approach: costs associated with physician travel and inconvenience, scheduling costs, and greater quantification of opportunity costs are
possible examples. Attention should also be focused on the determination of travel times, because they underlie the computed magnitude of all transportation costs. The definition of subregional boundaries is of particular concern. Use of an average distance approach as applied in this study expresses distance as a function of regional boundaries. As such, distances and travel time may vary accord-
217
ing to the selection of geographical regions used in the analysis. Capacity and demand constraints should also undergo reevaluation in future applications. Capacity of individual scanners is sensitive to ongoing technological development and the pattern of the learning and experience curve attending to operation of the equipment. Demand for future scanning services may also be expected to vary. Refinement of techniques and further technological developments will contribute to an evolution of the mix of cases that reap the greatest benefit from the equipment. Future trends in regulation, reimbursement, and consumer awareness also affect demand for the service. The breadth of existing health care legislation and the present structure of the health care industry present additional difficulties for the concrete application of this article's perspective. Planners in Health Systems Agencies, for example, now possess a mandate simply to limit new development. Current legislation enables them to limit the number of CT scanners in their localities, but not to determine where they are to be located. As our analysis indicates, limitations placed on the acquisition of new facilities in a given service region may not necessarily promote cost containment. Smaller numbers of facilities are quite compatible with higher costs. Additional problems arise from the fact that CT scanner deployment has already been quite extensive. While regulatory agencies may declare moritoria on purchases of CT scanners, they may not order the removal or relocation of existing facilities. The value of this discussion to planners and policy makers is largely as an approach to future developments. In an age of high technology medicine, it is inevitable that newer, more powerful, and more expensive devices and proce-
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dures will appear on the market in the closer coordination with health care years to come. Just as inevitable will be providers to make concrete use of the a continuation of the demand among theory and method we have proposed political figures and consumer advo- here. cates for better, more comprehensive delivery of services. To respond effectively to such demand, planners will ACKNOWLEDGEMENTS have to stay alert to new technological The authors wish to thank Michael J. developments before they are implemented by individual health care pro- Donnelly for important contributions viders, determine the set of needs that to the initial stages of this research and accompanies each high technology Richard W. Foster for useful comments offering, and make judgments about the on an earlier draft. Cindy Ostroff denecessary number of installations and serves special thanks for preparing the their optimal sitings in advance. graphic presentation. Clearly, planners will need to establish END NOTES 'The importance of providing a proper mix of services receives strong emphasis, for example, in the context of chronic disease. See Yelin et al. [13]. Yelin and his associates note that the availability of social services can lower utilization of medical services by helping chronic disease sufferers cope with their illnesses. Similarly, adequate medical care can reduce demand for social support services. The authors imply strongly that the proper combination o'f medical and social services is necessary to provide chronic disease patients with the most appropriate care at lowest cost. 2The estimate for critical care vehicles reflected the Chicago Fire Department's experience with mobile intensive care ambulance services. Costs were derived as follows: annual depreciation, $8,000; annual paramedic salaries, $30,000; maintenance/equipment replacement, $6,000; administrative overhead, $6,000; estimated total annual operating expenses, $50,000; average annual mileage, $25,000; and estimated cost per mile, $2.00. Cost estimates for the operation of private autos ($.40 per mile) and mass transportation ($.10 per mile) were derived similarly from estimated prevailing costs in the area. 3Federal planning guidelines released in September 1977 suggest an upper annual utilization limit of 4,000 scans. See [18]. Although recent planning guidelines cite 2,500 scans per year as a minimum level of utilization, 4,000 scans was considered an appropriate upper limit. Use of a capacity constraint approximating upper operating limits, as opposed to acceptable minimum levels of operation, simulates capital expenditures at more realistic levels. Moreover, low capacity will lead to more rapid achievement of capacity at a particular site requiring additional use of transportation services. Use of a higher capacity constraint is more conservative with respect to the overall level of expenditures generated. REFERENCES 1. Hyman, H.H. Health
Planning: A Systematic Approach, p. 38. Germantown, MD:
Aspen Systems Corporation, 1976.
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2 O'Connor, J.T. Comprehensive health planning: Dreams and realities. Health and Society 52:397, Fall 1974 3. Inglehart, J.K. The cost and regulation of medical technology: Future policy directions. Health and Society 55:36, Winter 1977. 4. Warner, K.E. Treatment decision making in catastrophic illness. Medical Care 15:21, Jan. 1977. 5. Terris, M. The need for a national health program. Bulletin of the New York Academy of Medicine 18:73, Jan. 1972. 6. Aday, L.A. and R. Andersen. Access to Medical Care, p. 73. Ann Arbor: Health Admin-
istration Press, 1975. 7. Tarlov, A.R., B. Schwartz, and H.P. Greenwald. Innovation in regional health care: The academic medical center's prospects and problems. Working paper, University of Chi-
cago, 1978. 8. Wildavsky, A. Can Health Care Be Planned? 1976 Michael Davis Lecture, p. 8. Chicago: Center for Health Administration Studies, 1976. 9. Rockoff, S.D. The evolving role of computerized tomography in radiation oncology. Cancer 39(2):694, Feb. 1977. 10. Schwartz, H. The government puts a damper on the scanner bonanza. New York Times,
Dec. 8, 1977. 11. Shapiro, S.H. and S.M. Wyman. CAT fever. New England lournal of Medicine 294:954,
Apr. 22, 1976. 12. Phillips, D.F. and K. Lillie. Putting the leash on the CAT. Hospitals 50:45, July 1, 1976. 13. Yelin, E.H. et al. Social problems, services, and policy for persons with rheumatoid arthritis. Social Science and Medicine, in press. 14. McKeown, T. The Role of Medicine: Dream, Mirage or Nemesis? London: Nuffield Provincial Hospitals Trust, 1976. 15. Godber, G.E. McKeown's "The Role of Medicine": Comments from a former chief medical officer. Health and Society 55:376, Summer 1977. 16. Wagner, H.M. Principles of Management Science. Englewood Cliffs, NJ: Prentice-Hall, 1970. 17. American Hospital Association. CT Scanners: A Technical Report. Chicago: American Hospital Association, 1977. 18. National guidelines for health planning: Advance notice of proposed rolemaking. Federal Register 42(185):48, 505, Sept. 23, 1977. 19. Chicago Health Systems Agency, Inc. Project and Program Review Manual: Procedures and Criteria, 1978-1979. Chicago: Chicago Health Systems Agency, Inc., 1978.
